Details

sample36.0ms

Algorithm

intervals

Results

10.0ms	203×	body	80	valid
5.0ms	18×	body	2560	valid
3.0ms	14×	body	1280	valid
2.0ms	7×	body	5120	valid
1.0ms	4×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	5×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

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: 35.9b

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)))
1.5b	(- (sqrt (+ (* re re) (* im im))) re)
28.6b	(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)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
24.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (+ (* re re) (* im im)))

simplify106.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (100.0ms)

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

prune110.0ms

Filtered

66 candidates to 52 candidates (21.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	61	5	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	6	67

Merged error: 18.0b

Counts

67 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
4.4b	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
29.7b	(cbrt (+ (* re re) (* im im)))
29.7b	(cbrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`sqrt-prod`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-l` `flip-+` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 66

Calls

4 calls:

8.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
8.0ms	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
3.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series111.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
30.0ms	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
20.0ms	(cbrt (+ (* re re) (* im im)))
25.0ms	(cbrt (+ (* re re) (* im im)))

simplify119.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	341	1002
1	1180	942
2	4515	900
3	5002	886

prune128.0ms

Filtered

78 candidates to 66 candidates (15.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	77	7	84

Merged error: 18.0b

Counts

84 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

5.0b	(exp (log (cbrt (+ (* re re) (* im im)))))
12.5b	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (exp (log (cbrt (+ (* re re) (* im im))))))) re)
29.7b	(cbrt (+ (* re re) (* im im)))
29.7b	(cbrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

5.0ms	(exp (log (cbrt (+ (* re re) (* im im)))))
11.0ms	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (exp (log (cbrt (+ (* re re) (* im im))))))) re)
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(exp (log (cbrt (+ (* re re) (* im im)))))
28.0ms	(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (exp (log (cbrt (+ (* re re) (* im im))))))) re)
21.0ms	(cbrt (+ (* re re) (* im im)))
23.0ms	(cbrt (+ (* re re) (* im im)))

simplify85.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	320	797
1	953	727
2	3014	670
3	5002	638

prune143.0ms

Filtered

71 candidates to 63 candidates (11.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	71	7	78

Merged error: 18.0b

Counts

78 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

12.8b	(- (* (fabs (* (pow (cbrt (cbrt (+ (* re re) (* im im)))) 2) (cbrt (cbrt (+ (* re re) (* im im)))))) (sqrt (exp (log (cbrt (+ (* re re) (* im im))))))) re)
29.7b	(cbrt (+ (* re re) (* im im)))
29.7b	(cbrt (+ (* re re) (* im im)))
29.7b	(cbrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

12.0ms	(- (* (fabs (* (pow (cbrt (cbrt (+ (* re re) (* im im)))) 2) (cbrt (cbrt (+ (* re re) (* im im)))))) (sqrt (exp (log (cbrt (+ (* re re) (* im im))))))) re)
4.0ms	(cbrt (+ (* re re) (* im im)))
3.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series89.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* (fabs (* (pow (cbrt (cbrt (+ (* re re) (* im im)))) 2) (cbrt (cbrt (+ (* re re) (* im im)))))) (sqrt (exp (log (cbrt (+ (* re re) (* im im))))))) re)
20.0ms	(cbrt (+ (* re re) (* im im)))
20.0ms	(cbrt (+ (* re re) (* im im)))
20.0ms	(cbrt (+ (* re re) (* im im)))

simplify82.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	287	874
1	901	781
2	3124	713
3	5002	689

prune149.0ms

Filtered

63 candidates to 61 candidates (3.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	63	7	70

Merged error: 18.0b

Counts

70 → 7

regimes713.0ms

Accuracy

66.7% (6.4b remaining)

Error of 23.2b against oracle of 16.9b and baseline of 36.0b

bsearch50.0ms

Steps

Iters	Range		Point
11	-6.627074657995507e-303	5.476747414844188e-279	6.36710860681304e-310
11	-8.220740893054099e+177	-9.582283671458726e+153	-9.71254003645233e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	23
1	44	23
2	44	23

end0.0ms

sample917.0ms

Algorithm

intervals

Results

343.0ms	6637×	body	80	valid
150.0ms	505×	body	2560	valid
79.0ms	204×	body	5120	valid
77.0ms	326×	body	1280	valid
32.0ms	167×	body	640	valid
15.0ms	109×	body	320	valid
5.0ms	52×	body	160	valid

Details

sample36.0ms

simplify9.0ms

prune3.0ms

localize10.0ms

rewrite23.0ms

series47.0ms

simplify106.0ms

prune110.0ms

localize14.0ms

rewrite25.0ms

series111.0ms

simplify119.0ms

prune128.0ms

localize18.0ms

rewrite26.0ms

series94.0ms

simplify85.0ms

prune143.0ms

localize23.0ms

rewrite24.0ms

series89.0ms

simplify82.0ms

prune149.0ms

regimes713.0ms

bsearch50.0ms

simplify2.0ms

end0.0ms

sample917.0ms

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