Details

sample52.0ms

Algorithm

intervals

Results

34.0ms

622×

body

valid

simplify94.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

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)
1.3b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
3×	`unpow-prod-down` `pow-unpow`
2×	`sub-neg` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `distribute-lft-out` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

24.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
16.0ms	(* (* a a) (+ 1.0 a))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
11.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
46.0ms	(* (* a a) (+ 1.0 a))
96.0ms	(pow (+ (* a a) (* b b)) 2.0)
51.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify63.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	504	702
1	2520	622
2	5002	622

prune240.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (* b b) (- 1.0 (* 3.0 a)))
8.9b	(cbrt (+ (* a a) (* b b)))
8.9b	(cbrt (+ (* a a) (* b b)))
8.9b	(cbrt (+ (* a a) (* b b)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `cbrt-prod` `add-sqr-sqrt` `add-cbrt-cube`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`add-log-exp`
3×	`flip3-+` `pow1/3` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/`
1×	`flip3--` `associate-l` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

11.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
2.0ms	(cbrt (+ (* a a) (* b b)))
2.0ms	(cbrt (+ (* a a) (* b b)))
2.0ms	(cbrt (+ (* a a) (* b b)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
88.0ms	(cbrt (+ (* a a) (* b b)))
88.0ms	(cbrt (+ (* a a) (* b b)))
88.0ms	(cbrt (+ (* a a) (* b b)))

simplify39.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	277	537
1	1234	483
2	5001	474

prune311.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

8.2b	(sqrt (+ (* a a) (* b b)))
8.2b	(sqrt (+ (* a a) (* b b)))
8.9b	(cbrt (+ (* a a) (* b b)))
8.9b	(cbrt (+ (* a a) (* b b)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

3.0ms	(sqrt (+ (* a a) (* b b)))
4.0ms	(sqrt (+ (* a a) (* b b)))
2.0ms	(cbrt (+ (* a a) (* b b)))
2.0ms	(cbrt (+ (* a a) (* b b)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ (* a a) (* b b)))
35.0ms	(sqrt (+ (* a a) (* b b)))
94.0ms	(cbrt (+ (* a a) (* b b)))
94.0ms	(cbrt (+ (* a a) (* b b)))

simplify51.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	141	444
1	440	420
2	1469	416
3	5002	414

prune367.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

8.2b	(sqrt (+ (* a a) (* b b)))
8.9b	(cbrt (+ (* a a) (* b b)))
8.9b	(cbrt (+ (* a a) (* b b)))
13.5b	(cbrt (pow (sqrt (+ (* a a) (* b b))) 3))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
13×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-prod`
6×	`unpow-prod-down` `cbrt-div` `cube-prod`
5×	`pow1`
4×	`add-exp-log` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`pow1/3`
2×	`cube-div`
1×	`cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

3.0ms	(sqrt (+ (* a a) (* b b)))
2.0ms	(cbrt (+ (* a a) (* b b)))
2.0ms	(cbrt (+ (* a a) (* b b)))
5.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 3))

series260.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (+ (* a a) (* b b)))
93.0ms	(cbrt (+ (* a a) (* b b)))
93.0ms	(cbrt (+ (* a a) (* b b)))
34.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 3))

simplify87.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	238	528
1	788	525
2	2886	525
3	5002	525

prune413.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes152.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	36
1	40	36

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

20276×

body

valid