Details

sample37.0ms

Algorithm

intervals

Results

9.0ms	180×	body	80	valid
7.0ms	26×	body	2560	valid
5.0ms	15×	body	5120	valid
4.0ms	18×	body	1280	valid
2.0ms	10×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	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

prune2.0ms

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: 38.9b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.7b	(- (sqrt (+ (* re re) (* im im))) re)
28.7b	(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)))

series109.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* re re) (* im im))
48.0ms	(- (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (56.0ms)

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

prune123.0ms

Filtered

50 candidates to 38 candidates (76.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	6	51

Merged error: 18.3b

Counts

51 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
5.8b	(exp (log (sqrt (+ (* re re) (* im im)))))
18.3b	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
28.7b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
6.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
10.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series143.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
36.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
44.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify66.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	223	519
1	737	467
2	2078	451
3	5001	442

prune184.0ms

Filtered

76 candidates to 53 candidates (69.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	72	4	76
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	73	9	82

Merged error: 18.2b

Counts

82 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
6.3b	(pow (exp 1/2) (log (+ (* re re) (* im im))))
17.8b	(- (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)
29.9b	(log (+ (* re re) (* im im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`add-cube-cbrt`
8×	`add-log-exp`
7×	`pow1` `log-prod`
5×	`add-exp-log`
4×	`unpow-prod-up` `unpow-prod-down` `log-div` `pow-unpow` `pow-pow` `add-cbrt-cube` `difference-of-squares`
3×	`exp-prod` `flip3-+` `flip-+`
2×	`log-pow` `pow-sub` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `pow-exp` `sum-log` `flip--` `distribute-lft-out--`

Counts

4 → 68

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
6.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
9.0ms	(- (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)
4.0ms	(log (+ (* re re) (* im im)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* re re) (* im im))
92.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
83.0ms	(- (pow (exp 1/2) (log (+ (* re re) (* im im)))) re)
50.0ms	(log (+ (* re re) (* im im)))

simplify94.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	302	653
1	1000	609
2	3205	604
3	5001	604

prune229.0ms

Filtered

80 candidates to 59 candidates (73.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	77	12	89

Merged error: 18.1b

Counts

89 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

17.8b	(- (* (* (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im))))) (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) re)
29.9b	(log (+ (* re re) (* im im)))
29.9b	(log (+ (* re re) (* im im)))
29.9b	(log (+ (* re re) (* im im)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

31.0ms	(- (* (* (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im))))) (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) re)
4.0ms	(log (+ (* re re) (* im im)))
4.0ms	(log (+ (* re re) (* im im)))
4.0ms	(log (+ (* re re) (* im im)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (* (* (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im))))) (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) (cbrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) re)
47.0ms	(log (+ (* re re) (* im im)))
51.0ms	(log (+ (* re re) (* im im)))
46.0ms	(log (+ (* re re) (* im im)))

simplify124.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 4 (116.0ms)

Iter	Nodes	Cost
0	182	818
1	426	645
2	1123	607
3	4102	607
4	5002	587

prune251.0ms

Filtered

66 candidates to 53 candidates (80.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	66	12	78

Merged error: 18.1b

Counts

78 → 12

regimes546.0ms

Accuracy

56.7% (9.3b remaining)

Error of 26.3b against oracle of 17.0b and baseline of 38.4b

bsearch107.0ms

Steps

Iters	Range	Point
7	8.554373099101626e-290	2.7552220295623955e-288	1.1868703169839283e-289
9	-2.2365661558835998e-197	-6.33701187792121e-204	-3.196517835772386e-203
5	-2.1804788916246727e+94	-8.504827414387646e+93	-2.1469124341159173e+94

Iters

Range

Point

8.554373099101626e-290

2.7552220295623955e-288

1.1868703169839283e-289

-2.2365661558835998e-197

-6.33701187792121e-204

-3.196517835772386e-203

-2.1804788916246727e+94

-8.504827414387646e+93

-2.1469124341159173e+94

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	26
1	48	26

end0.0ms

sample928.0ms

Algorithm

intervals

Results

305.0ms	6067×	body	80	valid
184.0ms	662×	body	2560	valid
118.0ms	509×	body	1280	valid
102.0ms	287×	body	5120	valid
47.0ms	252×	body	640	valid
22.0ms	163×	body	320	valid
6.0ms	60×	body	160	valid