Details

sample29.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify10.0ms

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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 36.7b

Counts

2 → 1

localize16.0ms

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)
33.9b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite45.0ms

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))
10.0ms	(+ (+ (* x x) (* y y)) (* z z))
14.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
10.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series272.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* x x) (* y y))
35.0ms	(+ (+ (* x x) (* y y)) (* z z))
50.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
160.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (29.0ms)

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

prune234.0ms

Filtered

90 candidates to 71 candidates (78.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	85	5	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	85	6	91

Merged error: 18.5b

Counts

91 → 6

localize11.0ms

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 (/ 1 3.0)))
33.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`sqrt-prod`
17×	`*-un-lft-identity`
16×	`associate-r`
15×	`add-cube-cbrt`
13×	`times-frac`
11×	`add-log-exp`
9×	`pow1` `sqrt-div`
8×	`unswap-sqr`
6×	`add-exp-log` `associate-l` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`sum-log`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`+-commutative` `frac-times` `associate-*l/`
1×	`rem-sqrt-square` `associate-+l+` `sqrt-unprod` `associate-r/` `prod-exp` `-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 88

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
6.0ms	(+ (+ (* x x) (* y y)) (* z z))
13.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* x x) (* y y))
35.0ms	(+ (+ (* x x) (* y y)) (* z z))
159.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
95.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify45.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	354	986
1	1482	945
2	5001	924

prune229.0ms

Filtered

100 candidates to 70 candidates (70.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	100	6	106

Merged error: 18.5b

Counts

106 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.2b	(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0))
0.2b	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
33.9b	(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

526×	`times-frac`
405×	`sqrt-prod`
296×	`add-sqr-sqrt`
279×	`add-cube-cbrt` `*-un-lft-identity`
25×	`associate-/l*`
16×	`div-inv`
12×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
9×	`add-log-exp`
7×	`rem-sqrt-square`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`sum-log` `associate-/l/`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`+-commutative` `associate-+l+` `sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 382

Calls

4 calls:

6.0ms	(+ (+ (* x x) (* y y)) (* z z))
14.0ms	(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0))
9.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
21.0ms	(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0)))

series585.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (+ (* x x) (* y y)) (* z z))
200.0ms	(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0))
125.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
224.0ms	(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0)))

simplify115.0ms

Algorithm

egg-herbie

Counts

394 → 394

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	843	7611
1	3029	7053
2	5001	6932

prune610.0ms

Filtered

394 candidates to 171 candidates (43.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	391	3	394
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	391	9	400

Merged error: 18.4b

Counts

400 → 9

localize5.0ms

Local error

Found 1 expressions with local error:

0.3b	(* (* -1 x) (sqrt (/ 1 3.0)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

16×	`associate-r`
13×	`sqrt-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`distribute-lft-neg-out` `mul-1-neg` `sqrt-div` `associate-r/` `associate-l` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

8.0ms

(* (* -1 x) (sqrt (/ 1 3.0)))

series50.0ms

Counts

1 → 3

Calls

1 calls:

50.0ms

(* (* -1 x) (sqrt (/ 1 3.0)))

simplify80.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	196	188
1	1003	156
2	3872	152
3	5001	145

prune57.0ms

Filtered

36 candidates to 23 candidates (63.9%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	31	5	36
Fresh	1	4	5
Picked	0	1	1
Done	0	3	3
Total	32	13	45

Merged error: 18.4b

Counts

45 → 13

regimes581.0ms

Accuracy

61.5% (7.5b remaining)

Error of 25.8b against oracle of 18.3b and baseline of 37.8b

bsearch65.0ms

Steps

Iters	Range		Point
7	2.114881440089652e+46	1.4672898867033973e+48	1.4468356973595232e+48
10	-1.2755199423227665e+123	-9.202938986759887e+109	-6.070944168763067e+121

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	13
1	34	13
2	34	13

end0.0ms

sample419.0ms

Algorithm

intervals

Results

257.0ms

8000×

body

valid