Details

sample60.0ms

Algorithm

intervals

Results

40.0ms

670×

body

valid

simplify103.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	53	15
1	161	15
2	459	15
3	1323	15
4	2992	15
5	5001	15

prune6.0ms

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: 0.2b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b	(* (* a a) (+ 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.5b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
42×	`associate-l`
40×	`*-un-lft-identity`
28×	`associate-+r+`
22×	`distribute-rgt-in` `distribute-lft-in`
18×	`add-cube-cbrt`
17×	`associate-r`
15×	`pow1` `add-exp-log` `unswap-sqr`
14×	`add-cbrt-cube`
10×	`swap-sqr`
9×	`+-commutative`
8×	`unpow-prod-down` `associate-+l+` `distribute-lft-out`
6×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `add-log-exp`
4×	`associate-*r/`
3×	`pow-unpow`
2×	`flip3-+` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `sqr-pow`

Counts

4 → 146

Calls

4 calls:

88.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
11.0ms	(* (* a a) (+ 1.0 a))
17.0ms	(pow (+ (* a a) (* b b)) 2.0)
14.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
47.0ms	(* (* a a) (+ 1.0 a))
104.0ms	(pow (+ (* a a) (* b b)) 2.0)
49.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify106.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	722	1111
1	3437	1031
2	5001	1031

prune399.0ms

Filtered

158 candidates to 100 candidates (63.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	153	5	158
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	5	159

Merged error: 0.0b

Counts

159 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* b b) (- 1.0 (* 3.0 a)))
0.5b	(* (* b b) (- 1.0 (* 3.0 a)))
7.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`associate-l`
34×	`*-un-lft-identity`
20×	`associate-r`
18×	`add-cube-cbrt`
16×	`pow1` `unswap-sqr`
14×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-prod`
8×	`swap-sqr`
6×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div` `associate-*r/` `distribute-lft-out` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `flip--` `flip-+`

Counts

4 → 128

Calls

4 calls:

14.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
17.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
82.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
84.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
48.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
172.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
173.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	398	1356
1	1832	1256
2	5001	1250

prune462.0ms

Filtered

140 candidates to 86 candidates (61.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	140	5	145

Merged error: 0.0b

Counts

145 → 5

localize32.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.4b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite332.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
20×	`sqrt-prod`
12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `sqrt-div` `distribute-lft-out`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-l` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

83.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
82.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
83.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
83.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series693.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
174.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
174.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
171.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify125.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	185	1580
1	687	1512
2	3527	1512
3	5001	1500

prune350.0ms

Filtered

80 candidates to 56 candidates (70.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	80	5	85

Merged error: 0.0b

Counts

85 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b	(* 2 (* (pow a 2) (pow b 2)))
3.1b	(* (pow a 2) (pow b 2))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
65×	`unswap-sqr`
53×	`associate-r`
39×	`add-exp-log`
36×	`unpow-prod-down`
30×	`*-un-lft-identity`
28×	`prod-exp` `unpow2` `sqr-pow`
21×	`associate-l`
16×	`add-cube-cbrt`
13×	`pow1`
12×	`pow-to-exp` `pow-exp`
11×	`pow-prod-down` `add-cbrt-cube` `add-log-exp`
8×	`pow-unpow`
7×	`distribute-lft-out`
4×	`sum-log` `cbrt-unprod`
3×	`+-commutative` `*-commutative`
2×	`associate-+r+` `pow-pow` `flip3-+` `flip-+`

Counts

4 → 167

Calls

4 calls:

38.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
30.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
25.0ms	(* 2 (* (pow a 2) (pow b 2)))
11.0ms	(* (pow a 2) (pow b 2))

series177.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
50.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
41.0ms	(* 2 (* (pow a 2) (pow b 2)))
32.0ms	(* (pow a 2) (pow b 2))

simplify82.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	566	1065
1	2445	894
2	5001	889

prune410.0ms

Filtered

179 candidates to 100 candidates (55.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	179	5	184

Merged error: 0.0b

Counts

184 → 5

regimes132.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	32
1	29	32

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.2s

20277×

body

valid