Details

sample35.0ms

Algorithm

intervals

Results

9.0ms	185×	body	80	valid
6.0ms	24×	body	2560	valid
4.0ms	17×	body	1280	valid
3.0ms	10×	body	5120	valid
2.0ms	13×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	4×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	24	8
2	30	8
3	35	8
4	35	8

prune2.0ms

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: 40.9b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.2b	(- (sqrt (+ (* re re) (* im im))) re)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`pow1`
6×	`*-un-lft-identity`
5×	`sqrt-prod` `add-log-exp`
4×	`add-cube-cbrt` `sqrt-div`
3×	`add-exp-log` `sqrt-pow1` `add-cbrt-cube`
2×	`flip3--` `pow1/2` `associate-*r/` `flip--` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `diff-log` `pow-prod-down` `flip-+` `distribute-lft-out--`

Counts

3 → 43

Calls

3 calls:

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)))

series250.0ms

Counts

3 → 9

Calls

3 calls:

167.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
44.0ms	(- (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify77.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	232	382
1	768	356
2	2506	346
3	5001	344

prune140.0ms

Filtered

52 candidates to 42 candidates (80.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	45	7	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	7	53

Merged error: 17.1b

Counts

53 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
5.0b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
22.5b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
32×	`times-frac`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
15×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`add-exp-log`
8×	`pow1` `associate-/l*`
6×	`add-cbrt-cube` `add-log-exp`
5×	`unpow2` `sqr-pow`
4×	`associate-/r*` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `sqrt-div` `div-exp` `flip-+`
2×	`pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
11.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
188.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
65.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	417	1078
1	1461	985
2	5001	978

prune262.0ms

Filtered

111 candidates to 78 candidates (70.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	110	8	118

Merged error: 5.7b

Counts

118 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
5.0b	(sqrt (* 2.0 (* (/ im (sqrt (+ (sqrt (+ (* re re) (* im im))) re))) (/ im (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))))
29.6b	(sqrt (+ (* re re) (* im im)))
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
8×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`sqrt-div` `sqrt-prod`
6×	`add-cube-cbrt` `add-log-exp`
5×	`sqrt-pow1`
4×	`add-exp-log` `associate-*r/` `add-cbrt-cube`
3×	`flip3-+` `pow1/2` `pow-prod-down` `flip-+`
2×	`rem-sqrt-square`
1×	`+-commutative` `frac-times` `associate-*l/` `sum-log` `distribute-lft-out`

Counts

4 → 57

Calls

4 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
21.0ms	(sqrt (* 2.0 (* (/ im (sqrt (+ (sqrt (+ (* re re) (* im im))) re))) (/ im (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
189.0ms	(sqrt (* 2.0 (* (/ im (sqrt (+ (sqrt (+ (* re re) (* im im))) re))) (/ im (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))))
34.0ms	(sqrt (+ (* re re) (* im im)))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	301	560
1	959	523
2	3254	513
3	5001	510

prune219.0ms

Filtered

69 candidates to 57 candidates (82.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	69	8	77

Merged error: 2.7b

Counts

77 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ im (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.4b	(* (sqrt 2.0) (fabs (/ im (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))))
0.7b	(+ (sqrt (+ (* re re) (* im im))) re)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
23×	`sqrt-prod`
21×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1` `associate-/r*`
6×	`associate-l` `add-log-exp`
5×	`distribute-lft-out`
4×	`sqrt-div`
3×	`flip3-+` `associate-r` `flip-+` `associate-/l*`
2×	`associate-/r/` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 94

Calls

4 calls:

10.0ms	(/ im (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
5.0ms	(* (sqrt 2.0) (fabs (/ im (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ im (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
40.0ms	(* (sqrt 2.0) (fabs (/ im (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))))
48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify46.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	409	1136
1	1471	1039
2	5001	1016

prune265.0ms

Filtered

106 candidates to 76 candidates (71.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	106	8	114

Merged error: 0.1b

Counts

114 → 8

regimes198.0ms

Accuracy

51.6% (17.8b remaining)

Error of 18.3b against oracle of 0.4b and baseline of 37.3b

bsearch187.0ms

Steps

Iters	Range		Point
8	2.1558392991063154e+98	3.0943356273139873e+102	2.1537425348704007e+102
9	-1.0921927090926265e-299	-4.707778381284133e-306	-5.158818445808552e-304
6	-6.699760191485107e-158	-1.388315075739649e-158	-1.4047799893311319e-158
9	-5.7624267828213205e+137	-6.4141430665981575e+128	-6.254434311354175e+129

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	45
1	64	45

end0.0ms

sample900.0ms

Algorithm

intervals

Results

301.0ms	6087×	body	80	valid
185.0ms	684×	body	2560	valid
104.0ms	472×	body	1280	valid
87.0ms	270×	body	5120	valid
48.0ms	280×	body	640	valid
17.0ms	131×	body	320	valid
7.0ms	76×	body	160	valid