Details

sample36.0ms

Algorithm

intervals

Results

12.0ms	193×	body	80	valid
5.0ms	19×	body	2560	valid
4.0ms	17×	body	1280	valid
3.0ms	8×	body	5120	valid
2.0ms	13×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	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

Filtered

1 candidates to 0 candidates (0.0%)

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: 40.7b

Counts

2 → 1

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)))
0.3b	(+ (sqrt (+ (* re re) (* im im))) re)
31.2b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

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

series292.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* re re) (* im im))
175.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	296	446
1	1086	401
2	3561	382
3	5001	381

prune209.0ms

Filtered

79 candidates to 69 candidates (87.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	74	5	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	5	80

Merged error: 6.9b

Counts

80 → 5

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

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:

5.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
3.0ms	(+ (hypot re im) re)

series248.0ms

Counts

2 → 6

Calls

2 calls:

189.0ms	(sqrt (* 2.0 (+ (hypot re im) re)))
59.0ms	(+ (hypot re im) re)

simplify52.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (48.0ms)

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

prune96.0ms

Filtered

38 candidates to 34 candidates (89.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	35	3	38
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	36	7	43

Merged error: 6.8b

Counts

43 → 7

localize9.0ms

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)))
15.3b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite11.0ms

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`
1×	`pow-prod-down` `fma-udef`

Counts

4 → 53

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
3.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
5.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series555.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (hypot re im))
87.0ms	(sqrt (hypot re im))
241.0ms	(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
138.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify79.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	194	379
1	555	327
2	2601	302
3	5001	300

prune183.0ms

Filtered

65 candidates to 52 candidates (80.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	62	3	65
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	63	9	72

Merged error: 6.8b

Counts

72 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
15.3b	(fma (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) re)

rewrite11.0ms

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)

series516.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))
111.0ms	(cbrt (hypot re im))
110.0ms	(cbrt (hypot re im))
163.0ms	(fma (sqrt (hypot re im)) (* (fabs (cbrt (hypot re im))) (sqrt (cbrt (hypot re im)))) re)

simplify40.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	294	623
1	1111	567
2	5001	546

prune273.0ms

Filtered

76 candidates to 66 candidates (86.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	77	8	85

Merged error: 6.8b

Counts

85 → 8

regimes103.0ms

Accuracy

30% (4.0b remaining)

Error of 11.8b against oracle of 7.7b and baseline of 13.5b

bsearch69.0ms

Steps

Iters	Range		Point
10	-2.464113685665428e+23	-26272724.29775533	-2.335384809104521e+22

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	13
1	29	13
2	29	13

end0.0ms

sample924.0ms

Algorithm

intervals

Results

290.0ms	5986×	body	80	valid
194.0ms	687×	body	2560	valid
112.0ms	489×	body	1280	valid
102.0ms	301×	body	5120	valid
52.0ms	291×	body	640	valid
24.0ms	162×	body	320	valid
8.0ms	84×	body	160	valid