Details

sample393.0ms

Algorithm

intervals

Results

47.0ms	76×	body	1280	valid
22.0ms	259×	body	80	valid
21.0ms	54×	body	640	valid
8.0ms	27×	body	320	valid
1.0ms	7×	body	160	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	35	21
1	63	17
2	98	17
3	217	17
4	895	17
5	5001	17

prune16.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (atan2 x.im x.re) y.im)
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.1b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `hypot-def`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
152.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify79.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	207	454
1	556	413
2	1286	411
3	2863	411
4	5002	411

prune381.0ms

Filtered

78 candidates to 66 candidates (84.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.2b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.8b	(* (atan2 x.im x.re) y.im)
30.6b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`pow1`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sqrt-prod` `log-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `flip3-+` `fma-neg` `diff-log` `prod-diff` `flip--` `flip-+` `hypot-def`

Counts

4 → 77

Calls

4 calls:

4.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
6.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
4.0ms	(* (atan2 x.im x.re) y.im)
4.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
87.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify81.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	320	595
1	1020	544
2	3156	516
3	5001	484

prune325.0ms

Filtered

89 candidates to 70 candidates (78.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
0.3b	(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
0.8b	(* (atan2 x.im x.re) y.im)
35.9b	(cbrt (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `cube-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `fma-udef` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

0.0ms	(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
2.0ms	(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
3.0ms	(* (atan2 x.im x.re) y.im)
2.0ms	(cbrt (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3))

series537.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
272.0ms	(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
16.0ms	(* (atan2 x.im x.re) y.im)
125.0ms	(cbrt (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3))

simplify49.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	299	737
1	1300	693
2	5002	683

prune322.0ms

Filtered

90 candidates to 61 candidates (67.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (fma y.re (log (hypot x.re x.im)) (- (log (exp (* (atan2 x.im x.re) y.im))))) 3)
0.8b	(* (atan2 x.im x.re) y.im)
4.4b	(log (exp (* (atan2 x.im x.re) y.im)))
26.8b	(cbrt (pow (fma y.re (log (hypot x.re x.im)) (- (log (exp (* (atan2 x.im x.re) y.im))))) 3))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-prod`
8×	`pow1`
7×	`add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `cube-prod`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `log-prod` `associate-r` `associate-l` `log-pow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `exp-prod` `exp-to-pow` `pow-pow` `pow1/3` `rem-log-exp` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

1.0ms	(pow (fma y.re (log (hypot x.re x.im)) (- (log (exp (* (atan2 x.im x.re) y.im))))) 3)
3.0ms	(* (atan2 x.im x.re) y.im)
1.0ms	(log (exp (* (atan2 x.im x.re) y.im)))
2.0ms	(cbrt (pow (fma y.re (log (hypot x.re x.im)) (- (log (exp (* (atan2 x.im x.re) y.im))))) 3))

series435.0ms

Counts

4 → 12

Calls

4 calls:

275.0ms	(pow (fma y.re (log (hypot x.re x.im)) (- (log (exp (* (atan2 x.im x.re) y.im))))) 3)
16.0ms	(* (atan2 x.im x.re) y.im)
20.0ms	(log (exp (* (atan2 x.im x.re) y.im)))
124.0ms	(cbrt (pow (fma y.re (log (hypot x.re x.im)) (- (log (exp (* (atan2 x.im x.re) y.im))))) 3))

simplify48.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	311	868
1	1307	733
2	5001	714

prune352.0ms

Filtered

96 candidates to 64 candidates (66.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 2.8b

regimes175.0ms

Accuracy

45.8% (1.7b remaining)

Error of 5.3b against oracle of 3.6b and baseline of 6.8b

bsearch44.0ms

Steps

Iters	Range		Point
4	-4.678818969655266e+173	-2.4722139571965733e+173	-3.919923789345116e+173

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	23
1	41	23
2	41	23

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.2s	2034×	body	1280	valid
703.0ms	8001×	body	80	valid
599.0ms	1490×	body	640	valid
191.0ms	690×	body	320	valid
58.0ms	324×	body	160	valid