Details

sample18.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize10.0ms

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)
34.0b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite142.0ms

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:

28.0ms	(+ (+ (* x x) (* y y)) (* z z))
7.0ms	(+ (* x x) (* y y))
75.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
29.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series285.0ms

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

simplify37.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (29.0ms)

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

prune231.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0)))
0.2b	(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
34.0b	(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
72×	`add-sqr-sqrt`
63×	`add-cube-cbrt` `*-un-lft-identity`
47×	`cbrt-prod`
46×	`sqrt-prod`
18×	`add-exp-log`
16×	`div-inv`
11×	`add-cbrt-cube`
10×	`associate-/l*`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`add-log-exp`
5×	`pow1` `rem-sqrt-square`
3×	`associate-/l/`
2×	`frac-2neg` `flip3-+` `prod-exp` `clear-num` `cbrt-unprod` `flip-+`
1×	`+-commutative` `sqrt-pow1` `pow1/2` `sqrt-div` `sum-log`

Counts

4 → 167

Calls

4 calls:

7.0ms	(+ (* x x) (* y y))
76.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0)))
83.0ms	(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
43.0ms	(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)))

series715.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* x x) (* y y))
202.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0)))
141.0ms	(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))
339.0ms	(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)))

simplify63.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	574	2995
1	2351	2794
2	5002	2767

prune550.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 18.5b

localize16.0ms

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))))
34.0b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite233.0ms

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×	`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` `frac-2neg` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 155

Calls

4 calls:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* x x) (* y y))
140.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
532.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
371.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify60.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	467	2452
1	1797	2356
2	5002	2337

prune564.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 18.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (sqrt (/ 1 (cbrt 3.0))) x)
0.4b	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (/ 1 (cbrt 3.0))) x))
1.0b	(/ 1 (cbrt 3.0))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
43×	`times-frac`
38×	`*-un-lft-identity`
36×	`add-cube-cbrt`
35×	`associate-l`
34×	`sqrt-prod`
23×	`cbrt-prod`
14×	`add-exp-log`
11×	`pow1` `add-cbrt-cube`
6×	`associate-/r*` `unswap-sqr`
5×	`sqrt-div`
4×	`associate-r` `pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod`
3×	`div-inv` `associate-/l*` `add-log-exp`
2×	`pow-flip` `div-exp` `*-commutative`
1×	`cbrt-undiv` `frac-times` `rec-exp` `frac-2neg` `pow1/3` `1-exp` `associate-*r/` `clear-num` `inv-pow`

Counts

3 → 118

Calls

3 calls:

24.0ms	(* (sqrt (/ 1 (cbrt 3.0))) x)
83.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (/ 1 (cbrt 3.0))) x))
10.0ms	(/ 1 (cbrt 3.0))

series268.0ms

Counts

3 → 7

Calls

3 calls:

114.0ms	(* (sqrt (/ 1 (cbrt 3.0))) x)
153.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (* (sqrt (/ 1 (cbrt 3.0))) x))
0.0ms	(/ 1 (cbrt 3.0))

simplify99.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	285	828
1	934	748
2	3616	685
3	5001	675

prune258.0ms

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 18.4b

regimes741.0ms

Accuracy

64.1% (6.9b remaining)

Error of 25.7b against oracle of 18.7b and baseline of 38.1b

bsearch51.0ms

Steps

Iters	Range		Point
8	3.260842031768285e+128	8.567969194639517e+132	2.8317233913665317e+132
5	-1.0741528074482224e+85	-3.1738050367834455e+84	-1.052922090158919e+85

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	20
1	50	20
2	53	20
3	53	20

end0.0ms

sample477.0ms

Algorithm

intervals

Results

257.0ms

8000×

body

valid