Details

sample399.0ms

Algorithm

intervals

Results

63.0ms	77×	body	1280	valid
41.0ms	249×	body	80	valid
24.0ms	44×	body	640	valid
6.0ms	15×	body	320	valid
3.0ms	10×	body	160	valid

simplify39.0ms

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

prune13.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 35.0b

Counts

2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (atan2 x.im x.re) y.im)
31.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.9b	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

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:

4.0ms	(* (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)))
9.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (atan2 x.im x.re) y.im)
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
156.0ms	(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify82.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	207	456
1	556	415
2	1286	411
3	2863	411
4	5002	411

prune340.0ms

Filtered

78 candidates to 66 candidates (84.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	5	79

Merged error: 18.3b

Counts

79 → 5

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))
0.3b	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.0b	(* (atan2 x.im x.re) y.im)
31.4b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

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))
5.0ms	(* (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)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
90.0ms	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
36.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify84.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (77.0ms)

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

prune268.0ms

Filtered

89 candidates to 70 candidates (78.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	89	5	94

Merged error: 3.9b

Counts

94 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im)))
0.0b	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
0.3b	(* (log (hypot x.re x.im)) y.re)
2.0b	(* (atan2 x.im x.re) y.im)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-l`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`exp-prod` `exp-sum`
2×	`sub-neg` `diff-log` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`flip3--` `exp-diff` `fma-neg` `log-pow` `flip--`

Counts

4 → 75

Calls

4 calls:

4.0ms	(exp (- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im)))
4.0ms	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
4.0ms	(* (log (hypot x.re x.im)) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)

series346.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(exp (- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im)))
128.0ms	(- (* (log (hypot x.re x.im)) y.re) (* (atan2 x.im x.re) y.im))
98.0ms	(* (log (hypot x.re x.im)) y.re)
19.0ms	(* (atan2 x.im x.re) y.im)

simplify81.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	265	517
1	869	474
2	2937	463
3	5001	458

prune232.0ms

Filtered

87 candidates to 66 candidates (75.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	86	6	92

Merged error: 3.9b

Counts

92 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (log (hypot x.re x.im)) y.re) (log (exp (* (atan2 x.im x.re) y.im)))))
0.3b	(* (log (hypot x.re x.im)) y.re)
2.0b	(* (atan2 x.im x.re) y.im)
2.9b	(log (exp (* (atan2 x.im x.re) y.im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `exp-sum` `add-cbrt-cube` `add-log-exp`
7×	`associate-l` `log-pow`
6×	`associate-r` `prod-diff`
5×	`exp-prod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod`
2×	`exp-to-pow` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`sub-neg` `exp-diff` `diff-log` `rem-log-exp`

Counts

4 → 80

Calls

4 calls:

6.0ms	(exp (- (* (log (hypot x.re x.im)) y.re) (log (exp (* (atan2 x.im x.re) y.im)))))
4.0ms	(* (log (hypot x.re x.im)) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
2.0ms	(log (exp (* (atan2 x.im x.re) y.im)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(exp (- (* (log (hypot x.re x.im)) y.re) (log (exp (* (atan2 x.im x.re) y.im)))))
98.0ms	(* (log (hypot x.re x.im)) y.re)
16.0ms	(* (atan2 x.im x.re) y.im)
16.0ms	(log (exp (* (atan2 x.im x.re) y.im)))

simplify73.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	273	599
1	848	474
2	2774	422
3	5001	420

prune236.0ms

Filtered

92 candidates to 65 candidates (70.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	4	4
Picked	1	0	1
Done	1	0	1
Total	93	5	98

Merged error: 3.9b

Counts

98 → 5

regimes144.0ms

Accuracy

46.5% (1.8b remaining)

Error of 5.2b against oracle of 3.5b and baseline of 6.8b

bsearch89.0ms

Steps

Iters	Range		Point
7	-3.2315068839947317e-16	-1.4790458398631249e-18	-3.1642853295886867e-16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	31
1	47	31
2	47	31

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.5s	1986×	body	1280	valid
988.0ms	7990×	body	80	valid
778.0ms	1429×	body	640	valid
248.0ms	640×	body	320	valid
71.0ms	279×	body	160	valid