Details

sample40.0ms

Algorithm

intervals

Results

21.0ms	95×	body	1280	valid
5.0ms	121×	body	80	valid
3.0ms	20×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	9×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	6

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: 16.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
2.2b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1`
3×	`associate-/r` `associate-/l`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `flip--` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

1.0ms	(hypot 1.0 x)
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series115.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot 1.0 x)
26.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
5.0ms	(/ 1.0 (hypot 1.0 x))
82.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	204	408
1	643	378
2	1992	376
3	5001	375

prune130.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	3	73

Merged error: 15.5b

Counts

73 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.7b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-/r` `associate-/l`
4×	`pow1` `associate-*r/` `associate--l+`
3×	`sub-neg`
2×	`cbrt-undiv` `distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `div-exp` `clear-num` `frac-sub` `flip--` `div-inv`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 84

Calls

4 calls:

8.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series69.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
5.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(/ 1.0 (hypot 1.0 x))
32.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify144.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	288	547
1	1035	512
2	4960	506
3	5001	506

prune207.0ms

Filtered

96 candidates to 68 candidates (70.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	94	5	99

Merged error: 15.5b

Counts

99 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.1b	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
1.7b	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`times-frac`
14×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
5×	`cube-div` `associate-*r/` `sqr-pow`
4×	`difference-of-squares`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `pow-exp` `rem-cube-cbrt`
2×	`flip3--` `pow-pow` `frac-2neg` `prod-exp` `clear-num` `frac-sub` `flip--` `cbrt-unprod` `div-inv`
1×	`difference-cubes` `cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `diff-log` `unpow3` `cube-prod` `pow-prod-down` `distribute-lft-out--`

Counts

4 → 99

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
8.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

series114.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
35.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
68.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

simplify61.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	344	689
1	1621	663
2	5002	663

prune372.0ms

Filtered

111 candidates to 79 candidates (71.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	110	6	116

Merged error: 15.2b

Counts

116 → 6

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 6)
0.1b	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
0.1b	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
1.7b	(- (pow (pow (* 1.0 (- 1.0 0.5)) 3) 3) (pow (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3) 3))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
39×	`sqr-pow`
36×	`difference-of-squares`
31×	`unpow-prod-down`
30×	`cube-prod`
22×	`add-exp-log`
17×	`*-un-lft-identity`
16×	`add-cbrt-cube`
13×	`pow1`
10×	`cube-div`
9×	`pow-unpow` `pow-exp`
7×	`add-cube-cbrt`
6×	`pow-pow` `associate-*r/` `prod-exp` `add-log-exp` `rem-cube-cbrt`
5×	`distribute-lft-out--`
4×	`cbrt-unprod`
3×	`pow-to-exp` `div-exp` `pow-prod-down`
2×	`cbrt-undiv` `cube-mult` `flip3--` `unpow3` `frac-sub` `flip--`
1×	`difference-cubes` `sub-neg` `diff-log`

Counts

4 → 124

Calls

4 calls:

9.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 6)
6.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
5.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
26.0ms	(- (pow (pow (* 1.0 (- 1.0 0.5)) 3) 3) (pow (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3) 3))

series216.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 6)
32.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
32.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
99.0ms	(- (pow (pow (* 1.0 (- 1.0 0.5)) 3) 3) (pow (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3) 3))

simplify93.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	457	1454
1	2108	1411
2	5001	1411

prune532.0ms

Filtered

136 candidates to 77 candidates (56.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	135	7	142

Merged error: 15.2b

Counts

142 → 7

regimes154.0ms

Accuracy

0% (0.3b remaining)

Error of 15.2b against oracle of 14.9b and baseline of 15.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	76
1	53	76

end0.0ms

sample1.0s

Algorithm

intervals

Results

600.0ms	2812×	body	1280	valid
157.0ms	4052×	body	80	valid
118.0ms	658×	body	640	valid
39.0ms	315×	body	320	valid
13.0ms	163×	body	160	valid