Details

sample28.0ms

Algorithm

intervals

Results

17.0ms

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: 38.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.4b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite62.0ms

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:

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

series276.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* x x) (* y y))
39.0ms	(+ (+ (* x x) (* y y)) (* z z))
47.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
164.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (32.0ms)

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

prune246.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.6b

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))
35.4b	(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
35.6b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.6b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite114.0ms

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:

63.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
21.0ms	(sqrt (* (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)))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
172.0ms	(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
99.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
100.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify50.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (37.0ms)

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

prune280.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.6b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow y 2) (pow z 2))
0.3b	(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
35.4b	(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
8×	`pow1`
7×	`add-sqr-sqrt` `distribute-lft-out`
6×	`associate-r`
5×	`add-exp-log` `add-cube-cbrt` `unpow-prod-down` `add-cbrt-cube` `add-log-exp`
4×	`associate-*r/`
3×	`flip3-+` `associate-l` `flip-+`
2×	`sqrt-pow1` `sqrt-div` `pow-prod-down`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `pow1/2` `prod-exp` `sum-log` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 51

Calls

3 calls:

9.0ms	(+ (pow y 2) (pow z 2))
108.0ms	(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
28.0ms	(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

series243.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (pow y 2) (pow z 2))
47.0ms	(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
165.0ms	(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	260	411
1	1384	379
2	5002	378

prune148.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 18.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.4b	(/ (+ (+ (* 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))))
35.4b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite132.0ms

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:

11.0ms	(+ (+ (* x x) (* y y)) (* z z))
29.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
67.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
19.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series867.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (+ (* x x) (* y y)) (* z z))
134.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
351.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
346.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify63.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (36.0ms)

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

prune570.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 18.5b

regimes465.0ms

Accuracy

62.9% (7.3b remaining)

Error of 25.0b against oracle of 17.7b and baseline of 37.5b

bsearch85.0ms

Steps

Iters	Range		Point
10	1.7826190976464906e+97	7.552700620960131e+107	1.3566371815103393e+105
5	-1.7575017886047935e+118	-4.9561533689906815e+117	-1.6174687293654252e+118

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	28
1	53	28
2	56	28
3	56	28

end0.0ms

sample725.0ms

Algorithm

intervals

Results

556.0ms

8000×

body

valid