Details

sample79.0ms

Algorithm

intervals

Results

63.0ms

650×

body

valid

simplify54.0ms

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

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

24.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
6.0ms	(* 4.0 (* b b))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series196.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
25.0ms	(* 4.0 (* b b))
103.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify110.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	249	342
1	939	315
2	3534	315
3	5001	315

prune138.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
14.9b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
14.9b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
14.9b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

123.0ms	(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
18.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
15.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
15.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series713.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
192.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
189.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
187.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify137.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	262	1815
1	942	1694
2	4261	1539
3	5001	1529

prune315.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 2 (* (pow a 2) (pow b 2)))
2.0b	(* (pow a 2) (pow b 2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log`
28×	`prod-exp`
23×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`unpow-prod-down`
12×	`pow-to-exp` `pow-exp`
11×	`associate-l`
10×	`unpow2` `sqr-pow`
9×	`associate-r` `add-cbrt-cube`
7×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `cbrt-unprod`
2×	`pow-prod-down` `*-commutative` `add-log-exp`

Counts

2 → 76

Calls

2 calls:

11.0ms	(* 2 (* (pow a 2) (pow b 2)))
9.0ms	(* (pow a 2) (pow b 2))

series73.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(* 2 (* (pow a 2) (pow b 2)))
37.0ms	(* (pow a 2) (pow b 2))

simplify35.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	229	393
1	907	329
2	5002	318

prune155.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

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:

10.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
6.0ms	(* 4.0 (* b b))
31.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
9.0ms	(* (pow a 2) (pow b 2))

series163.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
25.0ms	(* 4.0 (* b b))
65.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
32.0ms	(* (pow a 2) (pow b 2))

simplify56.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (47.0ms)

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

prune234.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes106.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	27
1	19	27

end0.0ms

sample2.4s

Algorithm

intervals

Results

2.0s

20311×

body

valid