Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

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

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

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)
34.1b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite25.0ms

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:

4.0ms	(+ (* x x) (* y y))
6.0ms	(+ (+ (* x x) (* y y)) (* z z))
8.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series309.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* x x) (* y y))
36.0ms	(+ (+ (* x x) (* y y)) (* z z))
55.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
187.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (30.0ms)

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

prune215.0ms

Filtered

90 candidates to 71 candidates (78.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	6	91

Merged error: 16.5b

Counts

91 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
34.1b	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
6.0ms	(+ (+ (* x x) (* y y)) (* z z))
8.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
6.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

series286.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* x x) (* y y))
41.0ms	(+ (+ (* x x) (* y y)) (* z z))
49.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
170.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify42.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	310	539
1	1615	492
2	5001	492

prune137.0ms

Filtered

71 candidates to 50 candidates (70.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	71	6	77

Merged error: 16.5b

Counts

77 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
34.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite30.0ms

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:

4.0ms	(+ (* x x) (* y y))
6.0ms	(+ (+ (* x x) (* y y)) (* z z))
12.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* x x) (* y y))
42.0ms	(+ (+ (* x x) (* y y)) (* z z))
229.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
102.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify46.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (33.0ms)

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

prune219.0ms

Filtered

114 candidates to 73 candidates (64.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	111	9	120

Merged error: 16.4b

Counts

120 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* 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))))
34.1b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite55.0ms

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:

6.0ms	(+ (+ (* x x) (* y y)) (* z z))
9.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
23.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
7.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

215.0ms	(+ (+ (* x x) (* y y)) (* z z))
128.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
381.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
364.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify60.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (38.0ms)

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

prune496.0ms

Filtered

169 candidates to 131 candidates (77.5%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	166	3	169
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	166	12	178

Merged error: 16.4b

Counts

178 → 12

regimes484.0ms

Accuracy

63.9% (7.1b remaining)

Error of 25.3b against oracle of 18.2b and baseline of 37.9b

bsearch85.0ms

Steps

Iters	Range		Point
10	1.2564031447521028e+119	7.880168417706032e+134	4.534756621196405e+123
9	-1.5035025016881667e+117	-1.8873369306133463e+111	-4.203820128874726e+116

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

sample446.0ms

Algorithm

intervals

Results

279.0ms

8000×

body

valid