Details

sample18.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	7
1	27	7
2	33	7
3	34	7
4	34	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.0b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`sqrt-prod`
11×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `fma-def` `sum-log` `log1p-expm1-u`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`+-commutative` `rem-sqrt-square` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `associate-+l+` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

4 → 90

Calls

4 calls:

13.0ms	(+ (+ (* x x) (* y y)) (* z z))
3.0ms	(+ (* x x) (* y y))
30.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
17.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series284.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (+ (* x x) (* y y)) (* z z))
27.0ms	(+ (* x x) (* y y))
54.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
165.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	345	852
1	1445	759
2	5001	739

prune317.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (fma y y (* z z)))
0.3b	(* 0.3333333333333333 (fma x x (fma y y (* z z))))
34.9b	(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1`
7×	`add-sqr-sqrt`
5×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`expm1-log1p-u` `associate-r` `associate-l` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow-prod-down`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/2` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 45

Calls

3 calls:

0.0ms	(fma x x (fma y y (* z z)))
3.0ms	(* 0.3333333333333333 (fma x x (fma y y (* z z))))
2.0ms	(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

series288.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(fma x x (fma y y (* z z)))
61.0ms	(* 0.3333333333333333 (fma x x (fma y y (* z z))))
178.0ms	(sqrt (* 0.3333333333333333 (fma x x (fma y y (* z z)))))

simplify98.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	134	287
1	587	252
2	3406	252
3	5001	252

prune131.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.2b	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
0.4b	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
35.2b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
75×	`times-frac` `sqrt-prod`
53×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`cbrt-prod`
25×	`associate-r`
16×	`unswap-sqr`
10×	`associate-l`
9×	`pow1`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r*` `add-log-exp`
5×	`sqrt-div`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-/l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-times` `fma-def` `frac-2neg` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 164

Calls

4 calls:

3.0ms	(+ (* x x) (* y y))
33.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
70.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
16.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series870.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* x x) (* y y))
134.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
340.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
361.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	483	2512
1	1869	2385
2	5001	2351

prune649.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 15.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`add-sqr-sqrt` `times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-log-exp`
6×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `sum-log` `flip-+` `log1p-expm1-u`
2×	`+-commutative` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `associate-+l+` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `hypot-def` `div-inv`

Counts

4 → 115

Calls

4 calls:

13.0ms	(+ (+ (* x x) (* y y)) (* z z))
3.0ms	(+ (* x x) (* y y))
27.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
15.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (+ (* x x) (* y y)) (* z z))
30.0ms	(+ (* x x) (* y y))
241.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
105.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify52.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	348	1348
1	1426	1262
2	5002	1230

prune300.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.7b

regimes464.0ms

Accuracy

82.9% (2.6b remaining)

Error of 16.5b against oracle of 13.9b and baseline of 29.0b

bsearch78.0ms

Steps

Iters	Range		Point
9	1.0755322234657376e+139	2.5591709680677497e+144	2.5319878970433065e+144
7	-1.1362783514012957e+154	-1.414609756848473e+152	-1.1196640135653541e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	20
1	49	20
2	52	20
3	52	20

end0.0ms

sample437.0ms

Algorithm

intervals

Results

268.0ms

8000×

body

valid