Details

sample16.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
37.0b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite59.0ms

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:

11.0ms	(+ (+ (* x x) (* y y)) (* z z))
2.0ms	(+ (* x x) (* y y))
29.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
14.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series282.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (+ (* x x) (* y y)) (* z z))
27.0ms	(+ (* x x) (* y y))
54.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
166.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (32.0ms)

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

prune247.0ms

Filtered

90 candidates to 71 candidates (78.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.5b

localize12.0ms

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))
36.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
37.0b	(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

rewrite127.0ms

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:

65.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
16.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
29.0ms	(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
96.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
97.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
170.0ms	(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (34.0ms)

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

prune277.0ms

Filtered

110 candidates to 78 candidates (70.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 19.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
0.3b	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
36.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

102×	`sqrt-prod`
73×	`add-sqr-sqrt`
44×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
25×	`associate-r`
16×	`sqrt-div`
12×	`unswap-sqr`
11×	`pow1`
9×	`associate-l`
6×	`add-exp-log` `add-cbrt-cube`
5×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`pow-prod-down`
2×	`frac-times` `associate-*l/` `div-inv`
1×	`sqrt-unprod` `associate-r/` `prod-exp` `-commutative` `cbrt-unprod`

Counts

4 → 130

Calls

4 calls:

18.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
75.0ms	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
167.0ms	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
99.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
101.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	344	2189
1	1191	2100
2	5001	2081

prune575.0ms

Filtered

142 candidates to 95 candidates (66.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 19.5b

localize3.0ms

Local error

Found 1 expressions with local error:

0.2b	(* x (sqrt 0.3333333333333333))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`associate-r`
4×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
3×	`pow1` `add-exp-log` `associate-l` `add-cbrt-cube`
2×	`unswap-sqr`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `add-log-exp`

Counts

1 → 22

Calls

1 calls:

4.0ms

(* x (sqrt 0.3333333333333333))

series44.0ms

Counts

1 → 3

Calls

1 calls:

44.0ms

(* x (sqrt 0.3333333333333333))

simplify61.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	69	84
1	245	80
2	569	78
3	893	78
4	2001	78
5	5001	78

prune31.0ms

Filtered

25 candidates to 14 candidates (56.0%)

Pruning

13 alts after pruning (9 fresh and 4 done)

Merged error: 19.4b

regimes588.0ms

Accuracy

63.1% (7.2b remaining)

Error of 25.5b against oracle of 18.3b and baseline of 37.8b

bsearch80.0ms

Steps

Iters	Range		Point
8	3.4079781488170856e+86	1.0026163978470942e+90	1.332425947371264e+89
11	-9.916277796985818e+165	-4.657848749767963e+130	-7.973789795621918e+148

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	12
1	33	12
2	33	12

end0.0ms

sample420.0ms

Algorithm

intervals

Results

261.0ms

8000×

body

valid