Details

sample73.0ms

Algorithm

intervals

Results

56.0ms

742×

body

valid

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	8
1	41	8
2	67	8
3	119	8
4	309	8
5	1494	8
6	5001	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

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)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

26.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
2.0ms	(+ (* a a) (* b b))
6.0ms	(* 4.0 (* b b))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series219.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
26.0ms	(+ (* a a) (* b b))
23.0ms	(* 4.0 (* b b))
103.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify39.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	322	413
1	1353	379
2	5001	379

prune165.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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)))
2.5b	(* (pow a 2) (pow b 2))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
28×	`prod-exp`
25×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`unpow-prod-down`
12×	`pow-to-exp` `pow-exp`
11×	`-un-lft-identity` `associate-l*` `add-cbrt-cube` `add-log-exp`
10×	`unpow2` `sqr-pow`
9×	`add-cube-cbrt` `associate-r`
6×	`pow1`
4×	`sum-log` `cbrt-unprod`
2×	`+-commutative` `flip3-+` `pow-prod-down` `*-commutative` `flip-+`
1×	`associate-+r+` `distribute-lft-out`

Counts

4 → 101

Calls

4 calls:

17.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
6.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
10.0ms	(* 2 (* (pow a 2) (pow b 2)))
9.0ms	(* (pow a 2) (pow b 2))

series175.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
55.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
35.0ms	(* 2 (* (pow a 2) (pow b 2)))
37.0ms	(* (pow a 2) (pow b 2))

simplify57.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	375	699
1	1613	622
2	5001	616

prune250.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
0.0b	(* 2.0 (* (pow a 2) (pow b 2)))
0.0b	(* 4.0 (* b b))
2.5b	(* (pow a 2) (pow b 2))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-exp-log`
31×	`prod-exp`
27×	`add-sqr-sqrt`
17×	`unswap-sqr`
16×	`add-cbrt-cube`
14×	`unpow-prod-down` `associate-l`
12×	`pow-to-exp` `pow-exp`
11×	`pow1`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r*` `unpow2` `sqr-pow`
9×	`add-log-exp`
7×	`cbrt-unprod`
5×	`pow-prod-down`
3×	`sum-log` `*-commutative`
1×	`+-commutative` `associate-+l+` `flip3-+` `flip-+`

Counts

4 → 108

Calls

4 calls:

29.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
10.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
6.0ms	(* 4.0 (* b b))
9.0ms	(* (pow a 2) (pow b 2))

series164.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
36.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
31.0ms	(* 4.0 (* b b))
32.0ms	(* (pow a 2) (pow b 2))

simplify58.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	400	683
1	1741	575
2	5002	568

prune242.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

2.5b	(* (pow a 2) (pow b 2))
2.5b	(* (pow a 2) (pow b 2))
24.5b	(sqrt (+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b))))
24.5b	(sqrt (+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
32×	`unswap-sqr`
28×	`add-exp-log` `unpow-prod-down`
20×	`unpow2` `sqr-pow`
18×	`prod-exp`
16×	`associate-r` `associate-l`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow-to-exp` `pow-exp`
8×	`add-cbrt-cube`
6×	`pow1` `sqrt-prod`
4×	`sqrt-div` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 132

Calls

4 calls:

9.0ms	(* (pow a 2) (pow b 2))
9.0ms	(* (pow a 2) (pow b 2))
28.0ms	(sqrt (+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b))))
32.0ms	(sqrt (+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b))))

series322.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (pow a 2) (pow b 2))
38.0ms	(* (pow a 2) (pow b 2))
126.0ms	(sqrt (+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b))))
126.0ms	(sqrt (+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b))))

simplify48.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	294	968
1	1213	856
2	5002	834

prune408.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes39.0ms

Accuracy

0% (1.0b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 1.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	9
1	18	9

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.5s

20373×

body

valid