Details

sample366.0ms

Algorithm

intervals

Results

42.0ms	68×	body	1280	valid
25.0ms	255×	body	80	valid
21.0ms	54×	body	640	valid
5.0ms	3×	body	2560	valid
4.0ms	16×	body	320	valid
1.0ms	8×	body	160	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	31	21
1	53	20
2	84	20
3	203	20
4	879	20
5	5001	20

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 35.1b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (atan2 x.im x.re) y.im)
30.4b	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
16×	`sqrt-prod`
12×	`add-sqr-sqrt`
11×	`associate-l`
10×	`distribute-lft-out`
8×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
4×	`sqrt-div` `swap-sqr` `add-log-exp`
3×	`associate-r`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `sin-sum` `flip-+`
1×	`+-commutative` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.im)
24.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.im)
154.0ms	(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
44.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
47.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify83.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	193	485
1	488	448
2	1083	448
3	2716	448
4	5001	448

prune277.0ms

Filtered

79 candidates to 55 candidates (30.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	73	6	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	6	80

Merged error: 19.7b

Counts

80 → 6

localize31.0ms

Local error

Found 4 expressions with local error:

22.2b	(sin (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
24×	`sqrt-prod`
15×	`distribute-lft-out`
12×	`associate-l`
10×	`add-sqr-sqrt`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div` `swap-sqr`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 67

Calls

4 calls:

5.0ms	(sin (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
18.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
15.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(sin (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify68.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	126	449
1	278	425
2	608	423
3	1926	423
4	5002	423

prune341.0ms

Filtered

79 candidates to 54 candidates (31.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	79	6	85

Merged error: 19.7b

Counts

85 → 6

localize37.0ms

Local error

Found 4 expressions with local error:

31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
32×	`sqrt-prod`
20×	`distribute-lft-out`
16×	`associate-l`
12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `sqrt-div` `swap-sqr`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 80

Calls

4 calls:

15.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
19.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series155.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify129.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	86	476
1	202	464
2	465	464
3	1174	464
4	3616	464
5	5001	464

prune458.0ms

Filtered

92 candidates to 60 candidates (34.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	92	6	98

Merged error: 19.7b

Counts

98 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (atan2 x.im x.re) y.re)
1.9b	(* (atan2 x.im x.re) y.im)
14.2b	(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ 1 x.re)))))
31.2b	(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
27×	`sin-diff`
26×	`log-prod` `associate--r+`
23×	`add-cube-cbrt`
18×	`times-frac`
13×	`distribute-rgt-in` `distribute-lft-in`
10×	`associate-l`
9×	`pow1`
8×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
6×	`associate-r`
5×	`distribute-lft-out`
4×	`add-log-exp`
2×	`sin-sum` `sqrt-div` `swap-sqr` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 92

Calls

4 calls:

3.0ms	(* (atan2 x.im x.re) y.re)
3.0ms	(* (atan2 x.im x.re) y.im)
19.0ms	(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ 1 x.re)))))
16.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

series164.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (atan2 x.im x.re) y.re)
17.0ms	(* (atan2 x.im x.re) y.im)
88.0ms	(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ 1 x.re)))))
41.0ms	(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify68.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	621	1175
1	1198	1137
2	2562	1085
3	5001	1025

prune270.0ms

Filtered

104 candidates to 56 candidates (46.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	96	8	104
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	98	12	110

Merged error: 14.0b

Counts

110 → 12

regimes492.0ms

Accuracy

73.2% (5.5b remaining)

Error of 17.9b against oracle of 12.5b and baseline of 32.9b

bsearch381.0ms

Steps

Iters	Range		Point
6	6.174355576258347e-57	7.945268834441626e-56	9.299895959750297e-57
10	6.739007507974489e-173	1.890718190471832e-162	2.798252125303727e-170
11	-3.0295251196676372e-294	2.480952709492434e-302	-5.47181818144811e-309

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	80
1	70	80

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	2264×	body	1280	valid
692.0ms	7949×	body	80	valid
613.0ms	1491×	body	640	valid
161.0ms	561×	body	320	valid
79.0ms	51×	body	2560	valid
45.0ms	233×	body	160	valid