Details

sample38.0ms

Algorithm

intervals

Results

9.0ms	184×	body	80	valid
8.0ms	28×	body	2560	valid
4.0ms	19×	body	1280	valid
2.0ms	7×	body	5120	valid
2.0ms	10×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	4×	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

prune3.0ms

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: 39.7b

Counts

2 → 1

localize11.0ms

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)))
1.6b	(- (sqrt (+ (* re re) (* im im))) re)
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

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))
12.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

series51.0ms

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

simplify105.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (98.0ms)

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

prune136.0ms

Filtered

52 candidates to 66 candidates (-26.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	58	8	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	8	67

Merged error: 22.2b

Counts

67 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
9.3b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite41.0ms

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:

15.0ms	(* (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)))

series26.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify48.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (34.0ms)

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

prune140.0ms

Filtered

72 candidates to 138 candidates (-91.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	138	8	146

Merged error: 22.2b

Counts

146 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

14.9b	(- (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (* (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (sqrt (+ (* re re) (* im im))))))) re)
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

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:

22.0ms	(- (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (* (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (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)))

series27.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4) (* (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (sqrt (+ (* re re) (* im im))))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	158	715
1	473	608
2	1783	574
3	5001	571

prune141.0ms

Filtered

56 candidates to 69 candidates (-23.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	69	8	77

Merged error: 22.2b

Counts

77 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

4.5b	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
9.3b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.3b	(sqrt (+ (* re re) (* im im)))
29.3b	(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	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
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	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
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)))

simplify108.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 4 (100.0ms)

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

prune234.0ms

Filtered

58 candidates to 73 candidates (-25.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	71	10	81

Merged error: 22.2b

Counts

81 → 10

regimes322.0ms

Accuracy

43.7% (12.2b remaining)

Error of 29.3b against oracle of 17.2b and baseline of 38.8b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	36
1	48	36

end0.0ms

sample1.1s

Algorithm

intervals

Results

326.0ms	6068×	body	80	valid
208.0ms	676×	body	2560	valid
114.0ms	464×	body	1280	valid
109.0ms	294×	body	5120	valid
57.0ms	261×	body	640	valid
23.0ms	159×	body	320	valid
8.0ms	78×	body	160	valid

Details

sample38.0ms

simplify6.0ms

prune3.0ms

localize11.0ms

rewrite31.0ms

series51.0ms

simplify105.0ms

prune136.0ms

localize16.0ms

rewrite41.0ms

series26.0ms

simplify48.0ms

prune140.0ms

localize19.0ms

rewrite35.0ms

series27.0ms

simplify56.0ms

prune141.0ms

localize17.0ms

rewrite40.0ms

series27.0ms

simplify108.0ms

prune234.0ms

regimes322.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample1.1s

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