Details

sample35.0ms

Algorithm

intervals

Results

11.0ms	215×	body	80	valid
4.0ms	14×	body	2560	valid
3.0ms	13×	body	1280	valid
2.0ms	6×	body	5120	valid
1.0ms	6×	body	640	valid
0.0ms	2×	body	320	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

prune8.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 37.5b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(- (sqrt (+ (* re re) (* im im))) re)
0.2b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
29.5b	(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:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series37.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
23.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify89.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	234	381
1	812	362
2	3077	355
3	5001	353

prune98.0ms

Filtered

52 candidates to 42 candidates (19.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	47	5	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	5	53

Merged error: 19.7b

Counts

53 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
4.5b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.5b	(sqrt (+ (* re re) (* im im)))
29.5b	(sqrt (+ (* re re) (* im im)))

rewrite45.0ms

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:

17.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
15.0ms	(- (* (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)))

series26.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (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)))

simplify47.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (34.0ms)

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

prune130.0ms

Filtered

138 candidates to 75 candidates (45.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	137	6	143

Merged error: 19.7b

Counts

143 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

4.5b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
5.1b	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
29.5b	(sqrt (+ (* re re) (* im im)))
29.5b	(sqrt (+ (* re re) (* im im)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`sqrt-prod` `add-log-exp`
4×	`add-exp-log` `log-prod` `exp-prod` `sqrt-div` `exp-sum` `add-cbrt-cube`
2×	`rem-sqrt-square` `log-div` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `exp-diff` `flip--` `flip-+` `difference-of-squares`
1×	`sub-neg` `diff-log` `log-pow` `rem-exp-log`

Counts

4 → 61

Calls

4 calls:

15.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
16.0ms	(exp (log (- (* (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)))

series26.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
8.0ms	(exp (log (- (* (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)))

simplify110.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 4 (102.0ms)

Iter	Nodes	Cost
0	191	746
1	442	597
2	1109	556
3	3525	548
4	5002	542

prune119.0ms

Filtered

73 candidates to 58 candidates (20.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	72	7	79

Merged error: 19.7b

Counts

79 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (sqrt (+ (* re re) (* im im))) re)
3.1b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
26.7b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
29.5b	(sqrt (+ (* re re) (* im im)))

rewrite38.0ms

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:

6.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
13.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
4.0ms	(sqrt (+ (* re re) (* im im)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify57.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	412	1076
1	1494	991
2	5002	987

prune148.0ms

Filtered

111 candidates to 78 candidates (29.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	2	2	4
Picked	1	0	1
Done	1	1	2
Total	110	8	118

Merged error: 4.0b

Counts

118 → 8

regimes249.0ms

Accuracy

53.9% (15.7b remaining)

Error of 20.2b against oracle of 4.6b and baseline of 38.6b

bsearch79.0ms

Steps

Iters	Range	Point
7	6.276619355487581e-81	1.061442330952725e-79	2.6090407096667592e-80
9	-7.635555118378116e-156	-1.8688797322818147e-162	-2.986641789409103e-158
6	-1.1073122392559708e+51	-1.555450845220469e+50	-1.0908449105214407e+51

Iters

Range

Point

6.276619355487581e-81

1.061442330952725e-79

2.6090407096667592e-80

-7.635555118378116e-156

-1.8688797322818147e-162

-2.986641789409103e-158

-1.1073122392559708e+51

-1.555450845220469e+50

-1.0908449105214407e+51

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	28
1	58	28
2	59	28
3	59	28

end0.0ms

sample933.0ms

Algorithm

intervals

Results

357.0ms	6672×	body	80	valid
148.0ms	494×	body	2560	valid
77.0ms	325×	body	1280	valid
68.0ms	181×	body	5120	valid
34.0ms	182×	body	640	valid
13.0ms	93×	body	320	valid
5.0ms	53×	body	160	valid

Details

sample35.0ms

simplify8.0ms

prune8.0ms

localize11.0ms

rewrite20.0ms

series37.0ms

simplify89.0ms

prune98.0ms

localize13.0ms

rewrite45.0ms

series26.0ms

simplify47.0ms

prune130.0ms

localize18.0ms

rewrite40.0ms

series26.0ms

simplify110.0ms

prune119.0ms

localize13.0ms

rewrite38.0ms

series45.0ms

simplify57.0ms

prune148.0ms

regimes249.0ms

bsearch79.0ms

simplify3.0ms

end0.0ms

sample933.0ms

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