Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

394×

body

valid

simplify288.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (7.0ms)

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

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))

simplify51.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

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

prune37.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite66.0ms

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:

3.0ms	(+ (* x y) (* z z))
13.0ms	(+ (+ (* x y) (* z z)) (* z z))
50.0ms	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

series137.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ (* x y) (* z z))
47.0ms	(+ (+ (* x y) (* z z)) (* z z))
50.0ms	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

simplify141.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (135.0ms)

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

prune144.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* x y) (* z z))) (cbrt (+ (* x y) (* z z))))
3.7b	(cbrt (+ (* x y) (* z z)))
3.7b	(cbrt (+ (* x y) (* z z)))
3.7b	(cbrt (+ (* x y) (* z z)))

rewrite27.0ms

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)))

series547.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (cbrt (+ (* x y) (* z z))) (cbrt (+ (* x y) (* z z))))
127.0ms	(cbrt (+ (* x y) (* z z)))
134.0ms	(cbrt (+ (* x y) (* z z)))
128.0ms	(cbrt (+ (* x y) (* z z)))

simplify50.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (38.0ms)

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

prune314.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x y) (* z z)) (* z z))
0.3b	(fma (sqrt (+ (+ (* x y) (* z z)) (* z z))) (sqrt (+ (+ (* x y) (* z z)) (* z z))) (* z z))
3.2b	(sqrt (+ (+ (* x y) (* z z)) (* z z)))
3.2b	(sqrt (+ (+ (* x y) (* z z)) (* z z)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

12.0ms	(+ (+ (* x y) (* z z)) (* z z))
0.0ms	(fma (sqrt (+ (+ (* x y) (* z z)) (* z z))) (sqrt (+ (+ (* x y) (* z z)) (* z z))) (* z z))
14.0ms	(sqrt (+ (+ (* x y) (* z z)) (* z z)))
17.0ms	(sqrt (+ (+ (* x y) (* z z)) (* z z)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (+ (* x y) (* z z)) (* z z))
185.0ms	(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)))
105.0ms	(sqrt (+ (+ (* x y) (* z z)) (* z z)))

simplify110.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	209	663
1	885	557
2	3767	541
3	5001	531

prune211.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes154.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	8	3
1	8	3

end0.0ms

sample558.0ms

Algorithm

intervals

Results

300.0ms

12311×

body

valid