Details

sample43.0ms

Algorithm

intervals

Results

26.0ms

690×

body

valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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:

2.0ms	(+ (* a a) (* b b))
6.0ms	(* 4.0 (* b b))
23.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series227.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* a a) (* b b))
31.0ms	(* 4.0 (* b b))
61.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
110.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 1 (9.0ms)

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

prune168.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 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))))
3.3b	(* (pow a 2) (pow b 2))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
16×	`unswap-sqr`
15×	`add-exp-log`
14×	`unpow-prod-down`
10×	`unpow2` `add-log-exp` `sqr-pow`
9×	`*-un-lft-identity` `prod-exp`
8×	`associate-r` `associate-l`
7×	`add-cube-cbrt`
6×	`pow-to-exp` `pow-exp`
5×	`add-cbrt-cube`
4×	`sum-log`
3×	`pow1`
2×	`+-commutative` `flip3-+` `flip-+`
1×	`associate-+r+` `pow-prod-down` `*-commutative` `cbrt-unprod` `distribute-lft-out`

Counts

3 → 76

Calls

3 calls:

18.0ms	(+ (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))))
13.0ms	(* (pow a 2) (pow b 2))

series334.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
252.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
31.0ms	(* (pow a 2) (pow b 2))

simplify51.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	327	556
1	1422	489
2	5001	476

prune190.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3)) (* 4.0 (* b b)))
0.2b	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
0.3b	(pow (+ (* a a) (* b b)) 2.0)
26.5b	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

29×	`unpow-prod-down`
20×	`cbrt-prod`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
14×	`cube-prod`
7×	`add-exp-log` `sqr-pow`
6×	`pow-unpow` `add-log-exp`
5×	`pow1` `pow-exp` `add-cbrt-cube`
3×	`pow-to-exp`
2×	`cube-mult` `pow-pow` `unpow3`
1×	`+-commutative` `flip3-+` `pow1/3` `sum-log` `rem-cbrt-cube` `flip-+` `rem-cube-cbrt`

Counts

4 → 90

Calls

4 calls:

60.0ms	(+ (cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3)) (* 4.0 (* b b)))
9.0ms	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
8.0ms	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

series418.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(+ (cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3)) (* 4.0 (* b b)))
117.0ms	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
98.0ms	(pow (+ (* a a) (* b b)) 2.0)
141.0ms	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

simplify57.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	367	843
1	1577	794
2	5001	788

prune214.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 4.0 (* b b))
0.0b	(+ (cbrt (pow (pow b 12.0) 1.0)) (* 4.0 (* b b)))
17.0b	(cbrt (pow (pow b 12.0) 1.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

7.0ms	(* 4.0 (* b b))
17.0ms	(+ (cbrt (pow (pow b 12.0) 1.0)) (* 4.0 (* b b)))
2.0ms	(cbrt (pow (pow b 12.0) 1.0))

series613.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* 4.0 (* b b))
244.0ms	(+ (cbrt (pow (pow b 12.0) 1.0)) (* 4.0 (* b b)))
344.0ms	(cbrt (pow (pow b 12.0) 1.0))

simplify78.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	274	339
1	858	315
2	2857	312
3	5002	309

prune136.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes116.0ms

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	15	8
1	15	8

end0.0ms

sample1.1s

Algorithm

intervals

Results

771.0ms

20581×

body

valid