Details

sample39.0ms

Algorithm

intervals

Results

24.0ms

628×

body

valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	26	8
1	51	8
2	88	7
3	153	7
4	357	7
5	1572	7
6	5002	7

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b	(+ (* a a) (* b b))
0.0b	(* 4.0 (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
8×	`fma-def` `add-log-exp`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `flip3-+` `sum-log` `flip-+` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `associate-r` `pow-exp` `*-commutative` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

7.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
4.0ms	(+ (* a a) (* b b))
6.0ms	(* 4.0 (* b b))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series225.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
30.0ms	(+ (* a a) (* b b))
25.0ms	(* 4.0 (* b b))
107.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify40.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	339	438
1	1458	396
2	5001	385

prune218.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)) 1.0)
0.0b	(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
0.0b	(* 2 (pow a 2))
0.9b	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
12×	`prod-diff`
11×	`add-log-exp`
9×	`add-exp-log`
8×	`associate-r`
6×	`add-cbrt-cube` `distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `fma-neg` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `associate-l` `prod-exp`
2×	`diff-log` `sum-log` `fma-udef` `distribute-lft-out--` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `associate-+l+` `flip3--` `flip3-+` `pow-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

8.0ms	(- (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)) 1.0)
5.0ms	(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
6.0ms	(* 2 (pow a 2))
1.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series206.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)) 1.0)
52.0ms	(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
25.0ms	(* 2 (pow a 2))
74.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify51.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	322	886
1	1427	748
2	5001	748

prune280.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.9b	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))
0.9b	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))
12.2b	(sqrt (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)))
12.2b	(sqrt (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt` `hypot-def`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`unpow-prod-down` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `fma-udef` `distribute-lft-out` `sqr-pow`

Counts

4 → 62

Calls

4 calls:

1.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))
1.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))
5.0ms	(sqrt (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)))
5.0ms	(sqrt (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))
74.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))
74.0ms	(sqrt (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)))
75.0ms	(sqrt (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)))

simplify72.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	107	598
1	402	576
2	1900	576
3	5001	572

prune296.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

10.7b	(sqrt (sqrt (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))))
12.2b	(sqrt (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)))
12.2b	(sqrt (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)))
12.2b	(sqrt (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
24×	`sqrt-prod`
17×	`*-un-lft-identity`
10×	`sqrt-div`
9×	`pow1` `add-cube-cbrt` `hypot-def`
7×	`sqrt-pow1`
5×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`unpow-prod-down` `sqr-pow`

Counts

4 → 87

Calls

4 calls:

6.0ms	(sqrt (sqrt (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))))
5.0ms	(sqrt (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)))
5.0ms	(sqrt (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)))
5.0ms	(sqrt (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(sqrt (sqrt (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))))
75.0ms	(sqrt (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)))
74.0ms	(sqrt (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)))
75.0ms	(sqrt (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)))

simplify65.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	122	950
1	351	909
2	1466	909
3	5001	898

prune415.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes40.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	8
1	15	8

end0.0ms

sample1.2s

Algorithm

intervals

Results

797.0ms

20319×

body

valid