Details

sample35.0ms

Algorithm

intervals

Results

10.0ms	198×	body	80	valid
6.0ms	20×	body	2560	valid
4.0ms	18×	body	1280	valid
3.0ms	8×	body	5120	valid
1.0ms	5×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify6.0ms

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

prune7.0ms

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: 36.8b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.7b	(- (sqrt (+ (* re re) (* im im))) re)
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

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

series45.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
25.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify106.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	260	458
1	982	428
2	3667	421
3	5001	420

prune123.0ms

Filtered

52 candidates to 66 candidates (-26.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	59	7	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	8	67

Merged error: 17.1b

Counts

67 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.8b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
51×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `difference-of-squares`

Counts

4 → 126

Calls

4 calls:

14.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
14.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series27.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify45.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	261	1112
1	935	975
2	5001	951

prune131.0ms

Filtered

73 candidates to 138 candidates (-89.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	5	6
Picked	0	1	1
Done	1	0	1
Total	139	7	146

Merged error: 17.1b

Counts

146 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

7.1b	(- (* (* (fabs (cbrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (cbrt (sqrt (+ (* re re) (* im im)))))) re)
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `add-cbrt-cube`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 57

Calls

4 calls:

14.0ms	(- (* (* (fabs (cbrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (cbrt (sqrt (+ (* re re) (* im im)))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* (* (fabs (cbrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (cbrt (sqrt (+ (* re re) (* im im)))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	250	734
1	809	669
2	2820	647
3	5001	632

prune125.0ms

Filtered

58 candidates to 69 candidates (-19.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	69	7	76

Merged error: 17.1b

Counts

76 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (sqrt (+ (* re re) (* im im))) re)
6.5b	(sqrt (* 2.0 (/ (+ 0 (pow im 2)) (+ (sqrt (+ (* re re) (* im im))) re))))
21.8b	(/ (+ 0 (pow im 2)) (+ (sqrt (+ (* re re) (* im im))) re))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `times-frac`
15×	`add-cube-cbrt`
11×	`distribute-lft-out`
8×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
3×	`sqrt-pow1` `sqrt-div`
2×	`pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `associate-*r/` `div-exp` `pow-prod-down` `clear-num` `sum-log` `div-inv`

Counts

4 → 79

Calls

4 calls:

6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
12.0ms	(sqrt (* 2.0 (/ (+ 0 (pow im 2)) (+ (sqrt (+ (* re re) (* im im))) re))))
14.0ms	(/ (+ 0 (pow im 2)) (+ (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
22.0ms	(sqrt (* 2.0 (/ (+ 0 (pow im 2)) (+ (sqrt (+ (* re re) (* im im))) re))))
10.0ms	(/ (+ 0 (pow im 2)) (+ (sqrt (+ (* re re) (* im im))) re))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	397	881
1	1554	792
2	5001	781

prune135.0ms

Filtered

71 candidates to 91 candidates (-28.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	90	8	98

Merged error: 6.9b

Counts

98 → 8

regimes247.0ms

Accuracy

45.4% (17.5b remaining)

Error of 24.4b against oracle of 6.9b and baseline of 39.0b

bsearch100.0ms

Steps

Iters	Range		Point
11	3.4035273351764263e+51	8.246976593957678e+75	2.390761022208988e+74
10	1.4140249174076056e-267	6.936990504008018e-253	6.806954305782995e-253
4	-1.3456703098874792e-49	-8.526402393323715e-50	-9.274449180684028e-50
11	-5.400427999982575e+167	-9.829567355960734e+143	-1.2377299438606592e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	40
1	72	40
2	73	40
3	73	40

end0.0ms

sample1.0s

Algorithm

intervals

Results

298.0ms	6058×	body	80	valid
184.0ms	648×	body	2560	valid
115.0ms	505×	body	1280	valid
97.0ms	288×	body	5120	valid
52.0ms	275×	body	640	valid
20.0ms	146×	body	320	valid
7.0ms	80×	body	160	valid

Details

sample35.0ms

simplify6.0ms

prune7.0ms

localize10.0ms

rewrite23.0ms

series45.0ms

simplify106.0ms

prune123.0ms

localize12.0ms

rewrite39.0ms

series27.0ms

simplify45.0ms

prune131.0ms

localize17.0ms

rewrite26.0ms

series51.0ms

simplify80.0ms

prune125.0ms

localize14.0ms

rewrite37.0ms

series46.0ms

simplify52.0ms

prune135.0ms

regimes247.0ms

bsearch100.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling