Details

sample18.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	7
1	22	7
2	24	7
3	24	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
38.1b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`sqrt-prod`
11×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`sum-log`
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 → 78

Calls

4 calls:

7.0ms	(+ (* x x) (* y y))
27.0ms	(+ (+ (* x x) (* y y)) (* z z))
70.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
30.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series248.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (* x x) (* y y))
32.0ms	(+ (+ (* x x) (* y y)) (* z z))
48.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
144.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	325	828
1	1345	761
2	5001	755

prune229.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
38.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
38.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
38.1b	(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
24×	`sqrt-prod`
22×	`times-frac` `associate-r`
21×	`add-cube-cbrt` `*-un-lft-identity`
17×	`sqrt-div`
11×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
6×	`flip3-+` `associate-l` `flip-+` `unswap-sqr`
4×	`frac-times` `sqrt-pow1` `associate-*l/` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square` `associate-*r/` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`cbrt-undiv` `div-exp` `*-commutative` `div-inv`

Counts

4 → 98

Calls

4 calls:

125.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
27.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
29.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
38.0ms	(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
94.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
93.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
149.0ms	(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	332	1540
1	1455	1341
2	5001	1274

prune277.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 21.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.3b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
38.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

7.0ms	(+ (* x x) (* y y))
28.0ms	(+ (+ (* x x) (* y y)) (* z z))
49.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
28.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (* x x) (* y y))
39.0ms	(+ (+ (* x x) (* y y)) (* z z))
206.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
90.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify46.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	330	1316
1	1338	1241
2	5002	1218

prune254.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 21.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.2b	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
0.5b	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
38.1b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite258.0ms

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` `add-log-exp`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r*`
5×	`sqrt-div`
4×	`div-inv`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `sum-log` `associate-/l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-times` `associate-+l+` `frac-2neg` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 157

Calls

4 calls:

28.0ms	(+ (+ (* x x) (* y y)) (* z z))
73.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
117.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
34.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series807.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (+ (* x x) (* y y)) (* z z))
118.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
313.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
336.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify57.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	433	2503
1	1579	2407
2	5001	2388

prune546.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 21.1b

regimes490.0ms

Accuracy

61.7% (7.4b remaining)

Error of 25.6b against oracle of 18.2b and baseline of 37.6b

bsearch90.0ms

Steps

Iters	Range		Point
11	1.1681615625015325e+106	4.8176863792130405e+125	4.548512359051216e+125
10	-2.4246649145524328e+112	-4.737880563320688e+100	-1.6534868728770253e+103

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	28
1	51	28
2	54	28
3	54	28

end0.0ms

sample466.0ms

Algorithm

intervals

Results

247.0ms

8000×

body

valid