Details

sample21.0ms

Algorithm

intervals

Results

11.0ms

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: 40.2b

Counts

2 → 1

localize9.0ms

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)
37.4b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite30.0ms

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:

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

series473.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (+ (* x x) (* y y)) (* z z))
26.0ms	(+ (* x x) (* y y))
47.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
360.0ms	(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

prune216.0ms

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: 17.3b

Counts

91 → 6

localize14.0ms

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))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
37.3b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
37.3b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

152×	`sqrt-prod`
122×	`add-sqr-sqrt`
84×	`times-frac`
55×	`*-un-lft-identity`
47×	`add-cube-cbrt`
25×	`associate-r` `associate-l`
24×	`unswap-sqr`
11×	`pow1`
9×	`sqrt-div`
6×	`add-exp-log` `add-cbrt-cube`
5×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
4×	`add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`flip3-+` `flip-+`
1×	`frac-times` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 156

Calls

4 calls:

7.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
25.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series491.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
157.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
94.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
99.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify65.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	391	2965
1	1318	2831
2	5002	2779

prune374.0ms

Filtered

168 candidates to 107 candidates (63.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	168	6	174

Merged error: 17.3b

Counts

174 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
37.3b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite27.0ms

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:

6.0ms	(+ (+ (* x x) (* y y)) (* z z))
4.0ms	(+ (* x x) (* y y))
9.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (+ (* x x) (* y y)) (* z z))
25.0ms	(+ (* x x) (* y y))
212.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
96.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify47.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (34.0ms)

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

prune219.0ms

Filtered

114 candidates to 72 candidates (63.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	111	9	120

Merged error: 17.2b

Counts

120 → 9

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:

5.0ms

(* x (sqrt 0.3333333333333333))

series43.0ms

Counts

1 → 3

Calls

1 calls:

43.0ms

(* x (sqrt 0.3333333333333333))

simplify68.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 2 (11.0ms)

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

prune29.0ms

Filtered

25 candidates to 14 candidates (56.0%)

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	20	5	25
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	20	14	34

Merged error: 17.2b

Counts

34 → 14

regimes616.0ms

Accuracy

59.8% (7.7b remaining)

Error of 26.5b against oracle of 18.7b and baseline of 38.0b

bsearch83.0ms

Steps

Iters	Range	Point
8	7.229723146941434e+91	2.9700228257164774e+96	2.9062712775060466e+96
7	-6.462637321531449e+77	-6.27097063247273e+75	-6.101025057096901e+77
5	-1.9168517598752196e+108	-8.938152136690335e+107	-1.2854725201619988e+108

Iters

Range

Point

7.229723146941434e+91

2.9700228257164774e+96

2.9062712775060466e+96

-6.462637321531449e+77

-6.27097063247273e+75

-6.101025057096901e+77

-1.9168517598752196e+108

-8.938152136690335e+107

-1.2854725201619988e+108

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	14
1	38	14
2	38	14

end0.0ms

sample548.0ms

Algorithm

intervals

Results

367.0ms

8000×

body

valid

Details

sample21.0ms

simplify7.0ms

prune2.0ms

localize9.0ms

rewrite30.0ms

series473.0ms

simplify41.0ms

prune216.0ms

localize14.0ms

rewrite51.0ms

series491.0ms

simplify65.0ms

prune374.0ms

localize10.0ms

rewrite27.0ms

series372.0ms

simplify47.0ms

prune219.0ms

localize3.0ms

rewrite5.0ms

series43.0ms

simplify68.0ms

prune29.0ms

regimes616.0ms

bsearch83.0ms

simplify2.0ms

end0.0ms

sample548.0ms

Profiling