Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	203×	body	80	valid
3.0ms	19×	body	1280	valid
3.0ms	14×	body	2560	valid
2.0ms	9×	body	5120	valid
1.0ms	6×	body	640	valid
0.0ms	5×	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

prune3.0ms

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: 36.8b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.5b	(- (sqrt (+ (* re re) (* im im))) re)
27.7b	(sqrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 41

Calls

3 calls:

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

series118.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* re re) (* im im))
47.0ms	(- (sqrt (+ (* re re) (* im im))) re)
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	172	305
1	661	282
2	1936	278
3	5002	276

prune135.0ms

Filtered

50 candidates to 38 candidates (76.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	44	6	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	6	51

Merged error: 17.0b

Counts

51 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.9b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
27.7b	(sqrt (+ (* re re) (* im im)))
27.7b	(sqrt (+ (* re re) (* im im)))

rewrite47.0ms

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:

16.0ms	(* (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)))

series159.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
50.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (34.0ms)

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

prune258.0ms

Filtered

138 candidates to 74 candidates (53.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	138	6	144

Merged error: 17.0b

Counts

144 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
28.6b	(cbrt (+ (* re re) (* im im)))
28.6b	(cbrt (+ (* re re) (* im im)))
28.6b	(cbrt (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

18.0ms	(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
96.0ms	(cbrt (+ (* re re) (* im im)))
95.0ms	(cbrt (+ (* re re) (* im im)))
98.0ms	(cbrt (+ (* re re) (* im im)))

simplify200.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 3 (179.0ms)

Iter	Nodes	Cost
0	287	1504
1	701	1463
2	3066	1446
3	5001	1379

prune254.0ms

Filtered

101 candidates to 65 candidates (64.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	101	6	107

Merged error: 17.0b

Counts

107 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

4.9b	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
6.9b	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
27.7b	(sqrt (+ (* re re) (* im im)))
27.7b	(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

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:

17.0ms	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
16.0ms	(- (* (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)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(exp (log (- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
48.0ms	(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
41.0ms	(sqrt (+ (* re re) (* im im)))
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify114.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 4 (106.0ms)

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

prune231.0ms

Filtered

73 candidates to 58 candidates (79.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	72	7	79

Merged error: 17.0b

Counts

79 → 7

regimes157.0ms

Accuracy

59.7% (8.6b remaining)

Error of 26.6b against oracle of 18.0b and baseline of 39.4b

bsearch89.0ms

Steps

Iters	Range		Point
9	-2.0137792410538042e-304	5.82714650145634e-306	2.51191004473425e-310
7	-4.710268451496385e+120	-1.940140840912921e+118	-2.775029731261256e+119

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	33
1	44	33

end0.0ms

sample697.0ms

Algorithm

intervals

Results

201.0ms	5962×	body	80	valid
148.0ms	725×	body	2560	valid
87.0ms	525×	body	1280	valid
68.0ms	277×	body	5120	valid
36.0ms	294×	body	640	valid
13.0ms	146×	body	320	valid
4.0ms	71×	body	160	valid