Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

394×

body

valid

simplify275.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (6.0ms)

Iter	Nodes	Cost
0	16	6
1	33	4
2	56	4
3	76	3
4	88	3
5	131	3
6	236	3
7	328	3
8	343	3
9	443	3
10	797	3
11	3499	3
12	5001	3

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x y) (* z z)) (* z z))
0.0b	(+ (* x y) (* z z))
0.1b	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
10×	`sum-log`
7×	`fma-def`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
3×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`associate-+l+`

Counts

3 → 51

Calls

3 calls:

12.0ms	(+ (+ (* x y) (* z z)) (* z z))
2.0ms	(+ (* x y) (* z z))
52.0ms	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

series128.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ (+ (* x y) (* z z)) (* z z))
38.0ms	(+ (* x y) (* z z))
45.0ms	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

simplify136.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (131.0ms)

Iter	Nodes	Cost
0	235	373
1	1084	317
2	4667	293
3	5001	292

prune152.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 3 (* z z) (* x y))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma 3 (* z z) (* x y))

series40.0ms

Counts

1 → 3

Calls

1 calls:

40.0ms

(fma 3 (* z z) (* x y))

simplify53.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	33	59
1	79	52
2	256	52
3	1025	52
4	5001	52

prune48.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* x y) (* z z))) (cbrt (+ (* x y) (* z z))))
2.3b	(cbrt (+ (* x y) (* z z)))
2.3b	(cbrt (+ (* x y) (* z z)))
2.3b	(cbrt (+ (* x y) (* z z)))

rewrite26.0ms

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×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `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 → 95

Calls

4 calls:

18.0ms	(* (cbrt (+ (* x y) (* z z))) (cbrt (+ (* x y) (* z z))))
2.0ms	(cbrt (+ (* x y) (* z z)))
2.0ms	(cbrt (+ (* x y) (* z z)))
2.0ms	(cbrt (+ (* x y) (* z z)))

series514.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (cbrt (+ (* x y) (* z z))) (cbrt (+ (* x y) (* z z))))
120.0ms	(cbrt (+ (* x y) (* z z)))
126.0ms	(cbrt (+ (* x y) (* z z)))
121.0ms	(cbrt (+ (* x y) (* z z)))

simplify44.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	295	1068
1	1172	1002
2	5001	923

prune287.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x y) (* z z))
0.3b	(fma (sqrt (+ (+ (* x y) (* z z)) (* z z))) (sqrt (+ (+ (* x y) (* z z)) (* z z))) (* z z))
1.8b	(sqrt (+ (+ (* x y) (* z z)) (* z z)))
1.8b	(sqrt (+ (+ (* x y) (* z z)) (* z z)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`+-commutative` `fma-def` `sum-log` `fma-udef`

Counts

4 → 60

Calls

4 calls:

2.0ms	(+ (* x y) (* z z))
0.0ms	(fma (sqrt (+ (+ (* x y) (* z z)) (* z z))) (sqrt (+ (+ (* x y) (* z z)) (* z z))) (* z z))
13.0ms	(sqrt (+ (+ (* x y) (* z z)) (* z z)))
14.0ms	(sqrt (+ (+ (* x y) (* z z)) (* z z)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* x y) (* z z))
184.0ms	(fma (sqrt (+ (+ (* x y) (* z z)) (* z z))) (sqrt (+ (+ (* x y) (* z z)) (* z z))) (* z z))
103.0ms	(sqrt (+ (+ (* x y) (* z z)) (* z z)))
104.0ms	(sqrt (+ (+ (* x y) (* z z)) (* z z)))

simplify100.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	227	611
1	921	525
2	3494	517
3	5001	508

prune192.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes166.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	3
1	8	3

end0.0ms

sample546.0ms

Algorithm

intervals

Results

299.0ms

12372×

body

valid